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Related Concept Videos

Beams01:30

Beams

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Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Prismatic Beams: Problem Solving01:15

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In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
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Principal Stresses in a Beam01:11

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In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
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Beams with Symmetric Loadings

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The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
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Related Experiment Video

Updated: Jan 28, 2026

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Simultaneous Generation of Multiple Three-Dimensional Tractor Curve Beams.

Jun Wu1, Xinquan Tang1, Jun Xia2

  • 1Joint International Research Laboratory of Information Display and Visualization, School of Electronic Science and Engineering, Southeast University, Nanjing, 210096, China.

Nanoscale Research Letters
|March 7, 2019
PubMed
Summary

Scientists developed a new method to create multiple, independent three-dimensional (3D) optical tractor beams. These beams can be shaped along complex curves and twisted, enabling advanced 3D manipulation and optical trapping applications.

Keywords:
3D tractor beamBeam shapingComputer holography

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Area of Science:

  • Optics and Photonics
  • Holography
  • Beam Shaping

Background:

  • Optical tractor beams can attract objects, with holographic technology enabling complex beam shaping for research and applications.
  • Current methods primarily generate two-dimensional (2D) and simple three-dimensional (3D) tractor beams, limiting further development.
  • Advanced beam shaping is crucial for expanding the utility of optical tractor beams.

Purpose of the Study:

  • To design and demonstrate multiple, independently controllable 3D optical tractor beams.
  • To enable arbitrary geometric path prescription and twisting for each individual beam.
  • To overcome the limitations of existing 2D and simple 3D tractor beam generation techniques.

Main Methods:

  • Utilizing computer-generated holograms (CGHs) to define the desired 3D curves for each tractor beam.
  • Multiplexing individual CGHs into a single phase-only hologram.
  • Encoding each CGH with a linear phase grating to spatially separate the resulting 3D beams in focal regions.

Main Results:

  • Successful experimental generation of multiple 3D optical tractor beams with independently controlled spatial locations.
  • Demonstration that each beam can follow arbitrary geometric curves and exhibit desired twisting.
  • Validation of the multiplexing and encoding technique for creating complex 3D beam arrangements.

Conclusions:

  • The developed method readily achieves the generation of 3D optical tractor beams in complex configurations.
  • This technique offers enhanced capabilities for applications requiring precise manipulation of multiple objects.
  • The approach is particularly suited for advanced applications like multiple micro-machining, optical trapping, and intricate 3D manipulation.